Subgroups — C₂×#1312 #11400

Order 256.

175 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
3	#1312	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	C₄	1	4	yes	—
5	C₂×C₄×C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
8	C₄×C₁₆	C₄	1	4	yes	—
9	C₄×C₁₆	C₂²	1	4	yes	—
10	C₈²	C₄	1	2	yes	—
11	C₈²	C₂²	1	2	yes	—
12	C₂²×C₈	C₈	1	2	yes	—
13	C₂²×C₈	C₈	1	2	yes	—
14	C₂²×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
16	C₂×C₁₆	—	2	8	no	—
17	C₂×C₁₆	C₂×C₄	1	8	yes	—
18	C₄×C₈	C₈	1	2	yes	—
19	C₄×C₈	C₈	1	2	yes	—
20	C₄×C₈	C₂×C₄	1	2	yes	—
21	C₄×C₈	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈	C₂×C₄	1	2	yes	—
23	C₄×C₈	C₂×C₄	1	2	yes	—
24	C₄×C₈	C₂³	1	1	yes	characteristic
25	C₂²×C₄	C₄²	1	1	yes	characteristic
26	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
27	C₂²×C₄	C₂×C₈	1	1	yes	characteristic
28	C₂×C₈	—	2	4	no	—
29	C₂×C₈	C₁₆	1	8	yes	complemented
30	C₂×C₈	C₄²	1	2	yes	—
31	C₂×C₈	C₂×C₈	1	4	yes	—
32	C₂×C₈	C₂×C₈	1	4	yes	—
33	C₂×C₈	M₁₆	1	8	yes	—
34	C₂×C₈	C₂²×C₄	1	2	yes	—
35	C₄²	C₄²	1	1	yes	characteristic
36	C₄²	C₂×C₈	1	1	yes	characteristic
37	C₄²	C₂×C₈	1	1	yes	characteristic
38	C₄²	C₂²×C₄	1	1	yes	characteristic
39	C₁₆	—	2	8	no	—
40	C₂³	C₄×C₈	1	1	yes	characteristic
41	C₂×C₄	C₄×C₈	1	1	yes	characteristic
42	C₂×C₄	C₄×C₈	1	1	yes	characteristic
43	C₂×C₄	C₄×C₈	1	1	yes	characteristic
44	C₂×C₄	#97	1	4	yes	—
45	C₂×C₄	C₂×C₁₆	1	4	yes	—
46	C₂×C₄	M₃₂	1	4	yes	—
47	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
48	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
49	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
50	C₈	—	2	4	no	—
51	C₈	#97	1	4	yes	—
52	C₈	C₂×C₁₆	1	8	yes	complemented
53	C₈	C₂×M₁₆	1	4	yes	—
54	C₂²	#322	1	2	yes	—
55	C₂²	C₄×C₁₆	1	2	yes	—
56	C₂²	#346	1	2	yes	—
57	C₂²	C₂×C₄×C₈	1	1	yes	characteristic
58	C₄	#322	1	2	yes	—
59	C₄	C₄×C₁₆	1	2	yes	—
60	C₄	#346	1	2	yes	—
61	C₄	C₂×#97	1	2	yes	—
62	C₄	C₂²×C₁₆	1	2	yes	—
63	C₄	C₂×M₃₂	1	2	yes	—
64	C₂	#1312	1	4	yes	direct product factor
65	C₂	C₂×#322	1	1	yes	characteristic
66	C₂	C₂×C₄×C₁₆	1	1	yes	characteristic
67	C₂	C₂×#346	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂²
commutator	C₂	C₂×C₄×C₁₆
Frattini, cosocle	C₄×C₈	C₂³
socle, prime radical	C₂³	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. #1312	C₂	direct (N × H)
29. C₂×C₈	C₁₆	semidirect
52. C₈	C₂×C₁₆	semidirect
64. C₂	#1312	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×C₁₆	2
C₂×C₈²	2
#1312	2

Subgroups — C2×#1312 #11400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1312 #11400